“The Pledge” is not lemon-fresh, though I suspect Jack Nicholson is being held together by space-age polymers.

Sean Penn directed this atmospheric thriller, and it has the makings of a fine piece of work. Nicholson is as good as ever (it’s one of his more sympathetic roles, too), and the supporting cast includes Benicio Del Toro, Vanessa Redgrave, Helen Mirren, Harry Dean Stanton and Mickey Rourke — each of whom shines despite appearing only briefly onscreen.

Nicholson’s character, homicide detective Jerry Black, is retiring reluctantly — so reluctantly he leaves his own farewell party to help cocky youngster Stan Krolak (Aaron Eckhart) on a murder investigation. A young girl has been found sexually assaulted and slaughtered, her body frozen out in the snowy woods.

None of the local police want to tell the victim’s family, so Jerry does it (this sounds suspect already). The mother (Patricia Clarkson), a rabidly religious woman, demands to know how anyone so evil could exist. Jerry assures her grimly that they do. He says he’ll find the killer. She makes him promise. He promises.

That would have been enough already. He’s sworn to apprehend the villain, and that’s why he insists on pursuing the case, even after he’s retired. But the film has the woman turning near-crazy on Jerry, making him swear on the salvation of his soul, using a wooden cross knickknack as an idol, that he will find the killer. It’s an utterly unbelievable moment.

On that basis, Jerry slowly and quietly becomes obsessed with the case, even though a suspect (Benicio Del Toro) was arrested and later committed suicide. Jerry has a “hunch” that they’d caught the wrong guy. It’s an awfully flimsy thing to base so much on (especially an entire movie), especially when a great deal of evidence points to the contrary.

Jerry’s hunch pays off, though, as a drawing made by the girl before she died suggests she may have known the killer. From a few circumstantial elements is drawn the conclusion that the man has killed three times already and will kill again within a year. Jerry must stop him, not just to save a life, but to save his own soul.

The devil, as they say, is in the details. Jerry buys a rural gas station (why?) and becomes friends and eventually housemates with a single mom named Lori (Robin Wright Penn) and her daughter Chrissy (Pauline Roberts). He suspects a local man, but never has his cop friends run a background check on him. The last victim was sexually assaulted, but was there no DNA evidence? If there wasn’t, fine, but the movie needs to let us know it at least recognized the possibility. The identity and fate of the killer is unsatisfying, too, and for the movie’s conclusion to make sense, you have to assume Jerry never heard about a significant highway accident that, had he known of it, would have settled his doubts.

Though Nicholson and company are stellar, the dreary film makes promises it doesn’t deliver on, pulling the rug out from under us without really letting us step on it in the first place. A little more deftness in the directing, and it could have been a marvelously unsettling work.

C+
(;
R, a barrage of harsh profanity near the end, and some gruesome violence.)